MATTER, SPACE, AND TIME 255 



''interval" s, we get a new kind of velocity //s. 

 Similarly momentum, which In the old mechanics 

 is Mv or M . //^, mass multiplied by velocity, may 

 be modified into a new kind of momentum, m . //s. 

 Here m is constant. But in physics it is, for the 

 present at all events, more convenient to keep 

 to the old definition of momentum as mass and 

 velocity. We then have — 



/ / / ,,./ 



m - = m - . - = M - J 

 s s i ^ 



where in. tjs is a modified mass, M, identical with 

 our old mass, no longer constant but dependent 

 on the motion through the observer's space and 

 time. It is easy to show mathematically that, 

 if momentum is conserved, 



M = 



where c is the constant velocity of light. 



This is the same law of Increase that was 

 calculated on the electro-magnetic theory by 

 Thomson, and verified by the experiments of 

 Kaufmann and others on /3 particles (page 237). 

 We now see that, while consistent with, It does 

 not necessarily verify, the electrical theory of 

 matter, since it follows also from the general 

 theory of relativity. If the observer moved with 

 the ^ particles, their mass as measured would 

 of course remain constant. The change Is a 

 consequence of the relative motion. 



The last equation can be put in the form — 



M = —. -^ / v\-h 



4-5) 



.,„,,--, 



